本文报道了实验与半解析结果，以阐明介电液体液滴撞击超疏水（SH）表面和亲水表面时的电流体动力学（EHD）。研究覆盖了较宽范围的 Weber 数（We）和电毛细管数（Cae），以探索液滴撞击 EHD 的不同机制。结果表明，在固定 We 为60时，随着电场强度增加，SH 表面上的液滴回弹受到抑制。在高 Cae 下，液滴并非如通常那样均匀径向收缩，而是在垂直于电场的方向上更快回缩，并沿电场方向铺展。这阻止了液滴积累实现回弹现象所需的足够动能。对于某些 We 和 Ohnesorge 数（Oh），液滴在回弹过程中表现出类似空翻的运动。随后，本文提出一个半解析模型来解释 SH 表面上由电场诱导的回弹现象。当 Cae 超过临界值4.0时，EHD 不稳定性通过边缘处尖顶的演化形成指状图案。此外，本文还讨论了亲水表面和 SH 表面上的铺展 EHD。在两种润湿性表面上且 We 固定时，铺展因子均随 Cae 增加呈上升趋势。我们建立了一个基于能量守恒的解析模型，用于预测最大铺展直径。该模型预测与实验观察结果具有相当好的一致性。最后，本文构建了一张相图，用于解释在较宽 We 和 Cae 范围内 SH 表面上的撞击后液滴动力学。
英文摘要：
In this article, we report experimental and semi analytical findings to elucidate the electrohydrodynamics EHD of a dielectric liquid droplet impact on superhydrophobic SH and hydrophilic surfaces. A wide range of Weber numbers We and electro-capillary numbers Cae is covered to explore the various regimes of droplet impact EHD. We show that for a fixed We 60, droplet rebound on SH surface is suppressed with increase of electric field intensity. At high Cae, instead of the usual uniform radial contraction, the droplets retract faster in orthogonal direction to the electric field and spread along the direction of the electric field. This prevents the accumulation of sufficient kinetic energy to achieve the droplet rebound phenomena. For certain values of We and Ohnesorge number Oh, droplets exhibit somersault like motion during rebound. Subsequently we propose a semi analytical model to explain the field induced rebound phenomenon on SH surfaces. Above a critical Cae 4.0, EHD instability causes fingering pattern via evolution of spire at the rim. Further, the spreading EHD on both hydrophilic and SH surfaces are discussed. On both wettability surfaces and for a fixed We, the spreading factor shows an increasing trend with increase in Cae. We have formulated an analytical model based on energy conservation to predict the maximum spreading diameter. The model predictions hold reasonably good agreement with the experimental observations. Finally, a phase map was developed to explain the post impact droplet dynamics on SH surfaces for a wide range of We and Cae.
Droplets move on substrates with a spatio-temporal wettability pattern as generated, for example, on light-switchable surfaces. To study such cases, we implement the boundary-element method to solve the governing Stokes equations for the fluid flow field inside and on the surface of a droplet and supplement it by the Cox-Voinov law for the dynamics of the contact line. Our approach reproduces the relaxation of an axisymmetric droplet in experiments, which we initiate by instantaneously switching the uniform wettability of a substrate quantified by the equilibrium contact angle. In a step profi…
Droplet motion over a surface with wettability gradient has been simulated using molecular dynamics (MD) simulation to highlight the underlying physics. GROMACS and Visual Molecular Dynamics (VMD) were used for simulation and intermittent visualization of the droplet configuration respectively. The simulations mimic experiments in a comprehensive manner wherein micro-sized droplets are propelled by surface wettability gradient against a number of retarding forces. The liquid-wall Lennard-Jones interaction parameter and the substrate temperature were varied to explore their effects on the three…
Despite a rigorous analysis of nonlinear electrohydrodynamics of a liquid droplet deformation in air, its influence on the surrounding gas phase has received less attention. We observed, air circulations created due to large deformation oscillations of a pendant water droplet subject to a resonating electric field act like a micro or mini blower in the air around the droplet. This is demonstrated through the deterioration of a strong electrostatic airborne particulate capture onto the droplet, when it is placed in an aerosol. Such strong local aerodynamic influence on the surrounding aerosol p…
We demonstrate \textit{bendotaxis}, a novel mechanism for droplet self-transport at small scales. A combination of bending and capillarity in a thin channel causes a pressure gradient that, in turn, results in the spontaneous movement of a liquid droplet. Surprisingly, the direction of this motion is always the same, regardless of the wettability of the channel. We use a combination of experiments at a macroscopic scale and a simple mathematical model to study this motion, focussing in particular on the time scale associated with the motion. We suggest that \emph{bendotaxis} may be a useful me…
In recent decades novel solid substrates have been designed which change their wettability in response to light or an electrostatic field. Here, we investigate a droplet on substrates with oscillating uniform wettability by varying minimium and maximum contact angles and frequency. To simulate this situation, we use our previous work [Grawitter and Stark, Soft Matter 17, 2454 (2021)], where we implemented the boundary element method in combination with the Cox-Voinov law for the contact-line velocity, to determine the fluid flow inside a droplet. After a transient regime the droplet performs s…
The article experimentally reveals and theoretically establishes the influence of electric fields on the evaporation kinetics of pendant droplets. It is shown that the evaporation kinetics of saline pendant droplets can be augmented by the application of an external alternating electric field. The evaporation behaviour is modulated by an increase in the field strength and frequency. The classical diffusion driven evaporation model is found insufficient in predicting the improved evaporation rates. The change in surface tension due to field constraint is insufficient for explaining the observed…
Effects of substrate temperature, substrate wettability and particles concentration are experimentally investigated for evaporation of a sessile water droplet containing colloidal particles. Time-varying droplet shapes and temperature of the liquid-gas interface are measured using high-speed visualization and infrared thermography, respectively. The motion of the particles inside the evaporating droplet is qualitatively visualized by an optical microscope and profile of final particle deposit is measured by an optical profilometer. On a non-heated hydrophilic substrate, a ring-like deposit for…
A classic result due to G.I.Taylor is that a drop placed in a uniform electric field becomes a prolate or oblate spheroid, which is axisymmetrically aligned with the applied field. We report an instability and symmetry-breaking transition to obliquely oriented, steady and unsteady shapes in strong fields. Our experiments reveal novel droplet behaviors such as tumbling, shape oscillations, and chaotic dynamics even under creeping flow conditions. A theoretical model, which includes anisotropy in the polarization relaxation due to drop asphericity and charge convection due to drop fluidity, eluc…
An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and the receding side -- to respective solutions of the problem on the microscale. On the microscale the velocity of movement is used as the small parameter of an asymptotic expansion. Matching gives the droplet shape, velocity of movement as a function of the imposed wettability gradient and droplet volume.
The directional movement and rebound behaviours of two droplets simultaneously impacting a designed flat surface with wettability difference is investigated based on the three-dimensional multi-relaxation-time pseudopotential lattice Boltzmann model. The effects of several factors, such as wettability difference, Weber number and droplet spacing on the directional movement and rebound behaviours are investigated in detail. The numerical results show that the unbalanced Young 's force caused by the wetting difference will cause the droplets to rebound or migrate laterally toward to the side wit…
The present article reports the hitherto unreported phenomenon of arrested evaporation dynamics in pendent droplets in an electric field ambience. The evaporation kinetics of pendant droplets of electrically conducting saline solutions in the presence of a transverse, alternating electric field is investigated experimentally. It has been observed that while increase of field strength arrests the evaporation, increment in field frequency has the opposite effect. The same has been explained on the solvation kinetics of the ions in the polar water. Theoretical analysis reveals that change in surf…
The present study deals with the dynamics of a double emulsion confined in a microchannel under the presence of a uniform electric field. Towards investigating the non-trivial electrohydrodynamics of a compound droplet, confined in between two parallel plate electrodes, a phase field approach has been adopted. Under the assumption of negligible fluid inertia and small shape deformation, an asymptotic model is also developed to predict the transient as well as the steady state droplet dynamics in the limiting case of an unbounded suspending medium. The phases involved are either assumed to be p…
Electrohydrodynamic (EHD) generation, a commonly used method in BioMEMS, plays a significant role in the pulsatile drug delivery system for a decade. In this paper, an EHD based drug delivery system is well designed, which can be used to generate a single drug droplet as small as 2.83 nL in 8.5 ms with a total device of 2\times2\times3 mm^3, and an external supplied voltage of 1500 V. Theoretically, we derive the expressions for the size and the formation time of a droplet generated by EHD method, while taking into account the drug supply rate, properties of liquid, gap between two electrodes,…
The present study deals with the numerical as well as asymptotic analysis of the electrohydrodynamic interaction between two deformable droplets in a confined shear flow. Considering both the phases as leaky dielectric, we have performed numerical simulations to study the effect of channel confinement on the drop trajectories in the presence of a uniform electric field. Two important varieties of motion are identified in the present analysis, namely (i) the reversing motion and (ii) the passing over motion. The study suggests that conversion of the passing over motion to the reversing motion o…
Dynamic Wettability Modulation of Textured, Soft and LIS Interfaces Using Electrowetting
School of Mechanical Sciences, Indian Institute of Technology (IIT) Goa（印度理工学院果阿分校机械科学学院）；Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur（印度理工学院卡拉格普尔分校机械工程系）
Surface wettability has a huge influence on its functional properties. For example, to minimize smudging, surfaces should be able to repel oil droplets. To quantify surface wettability, the most common approach is to measure the contact angles of a liquid droplet on the surface. While well-established and relatively easy to perform, contact angle measurements are crude and imprecise; moreover, they cannot spatially resolve surface heterogeneities that can contribute to surface fouling. To address these shortcomings, we report on using an Atomic Force Microscopy (AFM) technique to quantitativel…
The influence of miscibility and liquid wettability during droplet impact onto thin wall films is investigated experimentally. Despite similar liquid properties and impact conditions, differences in the splashing limit, the crown extension and the duration of the ascending phase are observed. These differences are related to the interfacial tension of the droplet/wall-film liquid pairs, which is linked to their miscibility and wettability. More precisely, by calculating the crown surface energy, we show that the energy stored in the interface between droplet and wall-film (if any) is not negli…
Would a raindrop impacting on a coarse beach behave differently from that impacting on a desert of fine sand? We study this question by a series of model experiments, where the packing density of the granular target, the wettability of individual grains, the grain size, the impacting liquid, and the impact speed are varied. We find that by increasing the grain size and/or the wettability of individual grains the maximum droplet spreading undergoes a transition from a capillary regime towards a viscous regime, and splashing is suppressed. The liquid-grain mixing is discovered to be the underlyi…
How to make small liquid droplets move spontaneously and directionally on solid surfaces is a challenge in lab-on-chip technologies, DNA analysis, and heat exchangers. The best-known mechanism, a wettability gradient, does not move droplets rapidly enough for most purposes and cannot move droplets smaller than a critical size defined by the contact angle hysteresis. Here we report on a mechanism using curvature gradients, which we show is particularly effective at accelerating small droplets, and works for both hydrophilic and hydrophobic surfaces. Experiments for water droplets on glass cones…
The classical wetting models, such as the Wenzel and Cassie-Baxter have been extensively used to quantify the wettability of laser-textured surfaces. However, these models do not provide any description of the corresponding droplet dynamics. In this work, we propose a detailed continuum-level modelling to study the wetting dynamics of a water droplet on Ti-6Al-4V alloy. The calculations are performed for flat surfaces and surfaces with various reliefs. The calculated evolutions of the droplet spreading parameter for flat surfaces, surfaces with triangular reliefs and one with two different per…
Experimental investigations were carried out to elucidate the role of surface wettability and inclination on the post impact dynamics of droplets. Maximum spreading diameter and spreading time were found to decrease with increasing inclination angle and normal Weber number for superhydrophobic surfaces. The experiments on SH surfaces were found to be in excellent agreement with an existing analytical model, incorporated with the modifications for the oblique impact conditions. Energy ratios and elongation factor were also measured for different inclination angles. On inclined SH surfaces, diff…
This study has numerically investigated the effect of surface wettability on two-phase immiscible flow and dynamics of droplet pinch-off in a T-junction microchannel using finite element method. A conservative level set method (CLSM) has been adopted to capture the interface topology in squeezing regime ($Ca_c <10^{-2}$) for wide flow rate ratio ($1/10 \leq Q_r \leq 10$) and contact angle ($120^{\circ} \leq θ\leq 180^{\circ}$). Based on the instantaneous phase profiles, droplet formation stages are classified as initial, filling, squeezing, pinch-off and stable droplet. Wettability effects are…
Post impingement morphology and dynamics of water droplets on convex cylindrical surfaces has been explored experimentally. Droplet impact and post-impact feature studies have been conducted on hydrophillic and superhydrophobic cylindrical surfaces. Effects of the impact Weber number and target-to-drop diameter ratio have been studied. The post-impact hydrodynamics have been quantified using the wetting fraction, the spreading factor and nondimensional film thickness at the north pole of the target. The observations reveal that the wetting fraction and spread factor increases with an increase …
Droplets confined in a microfluidic channel often exhibit intriguing shapes, primarily attributable to complex hydrodynamic interactions over small scales. We show that effect of varied substrate wettability conditions may further complicate these interactions remarkably, and often non-trivially. Our studies reveal that the combined influence of substrate wettability and fluidic confinement eventually culminates towards influencing the droplet transients, distortion of the local shear flow field, as well as drop stabilization against breakup or detachment, allowing one to develop different reg…
This paper reports the dynamic wetting behavior and heat transfer characteristics for impinging droplets on heated bi-phobic surfaces (superhydrophobic matrix with hydrophobic spots). A non-patterned superhydrophobic and a sticky hydrophobic surface acted as control wettability surfaces. As expected, differences in wetting and heat transfer dynamics were noticeable for all surfaces, with the most pronounced variation during the receding phase. During spreading, inertia from the impact dominated the droplet dynamics and heat transfer was dominated by convection at the contact line and internal …
The deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the Melcher-Taylor leaky dielectric model. The main assumption of the model is that any net charge in the system is concentrated on the interface between the two liquids as a result of the jump in Ohmic currents from the bulk. Upon application of the field, the drop can either attain a steady prolate or oblate shape with toroidal circulating flows both inside and outside arising from tangential stresses on the interface due to a…
The transport of small quantities of liquid on a solid surface is inhibited by the resistance to motion caused by the contact between the liquid and the solid. To overcome such resistance, motion can be externally driven through gradients in electric fields, but these all inconveniently involve the input of external energy. Alternatively, gradients in physical shape and wettability - the conical shape of cactus spines to create self-propelled motion. However, such self-propelled motion to date has limited success in overcoming the inherent resistance to motion of the liquid contact with the so…
Making liquid droplets move spontaneously on solid surfaces is a key challenge in lab-on-chip and heat exchanger technologies. The best-known mechanism, a wettability gradient, does not generally move droplets rapidly enough and cannot drive droplets smaller than a critical size. Here we report how a curvature gradient is particularly effective at accelerating small droplets, and works for both hydrophilic and hydrophobic surfaces. Experiments for water droplets on tapered surfaces with curvature radii in the sub-millimeter range show a maximum speed of 0.28 m/s, two orders of magnitude higher…
Droplet Impact on Microparticle Raft: Wettability, density and size govern splashing and microplastic ejection from rafts under raindrop impact
University College London（伦敦大学学院）；University of Oxford（牛津大学）；Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México（墨西哥国立自治大学材料研究所）
On Free Moving Micron-Sized Droplet-Particle Collisions
School of Chemical and Process Engineering, University of Leeds（利兹大学化学与工艺工程学院）；School of Natural Sciences, Department of Mathematics, University of Manchester（曼彻斯特大学自然科学学院数学系）；School of Mathematics, Statistics, Chemistry and Physics, Murdoch University（默多克大学数学、统计、化学和物理学院）
Modification and control over the vaporization kinetics of microfluidic droplets may have strong utilitarian implications in several scientific and technological applications. The article reports the control over the vaporization kinetics of pendent droplets under the influence of competing internal electrohydrodynamic and ferrohydrodynamic advection. Experimental and theoretical studies are performed and the morphing of vaporization kinetics of electrically conducting and paramagnetic fluid droplets using orthogonal electric and magnetic stimuli is established. Analysis of the observations re…
In this paper, the droplet impact dynamic behavior of droplet on Janus-textured heated substrates is numerically investigate by using the thermal Lattice Boltzmann method. The effect of several factors like the wettability, the Jakob number and the Weber number on the droplet impact dynamic behavior on Janus-textured heated surface are studied in detail. The simulation results show three types of boiling states, i.e., contact boiling, transition boiling and film boiling. The droplets in contact boiling state directionally migrate toward the denser region, while the droplets move toward the spa…
Asymmetric freezing of a sliding droplet on an inclined surface
Indian Institute of Technology Hyderabad（印度理工学院海德拉巴分校）；Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）；Indian Institute of Technology Ropar（印度理工学院罗帕尔分校）
Understanding the influence of hydrodynamic stresses and colloidal interactions between droplets and membranes will inform better engineered membrane surfaces and process conditions. Using a long-wave hydrodynamic description that incorporates wettability and electrostatic repulsion, we numerically investigate the influence of droplet shapes and membrane characteristics on the overall repulsion-attraction towards the membrane surface. A stability phase diagram classifies stable-unstable drop shapes and investigate whether there is reversible deposition of droplets onto the membrane.
Electrohydrodynamic instabilities of fluid-fluid interfaces can be exploited in various microfluidic applications in order to enhance mixing, replicate well-controlled patterns or generate drops of a particular size. In this work, we study the stability and dynamics of a system of three superimposed layers of two immiscible fluids subject to a normal electric field. Following the Taylor-Melcher leaky dielectric model, the bulk remains electroneutral while a net charge accumulates on the interfaces. The interfacial charge dynamics is captured by a conservation equation accounting for Ohmic cond…
Bumps are omnipresent from human skin to the geological structures on planets, which offer distinct advantages in numerous phenomena including structural color, drag reduction, and extreme wettability. Although the topographical parameters of bumps such as radius of curvature of convex regions significantly influence various phenomena including anti-reflective structures and contact time of impacting droplets, the effect of the detailed bump topography on growth and transport of condensates have not been clearly understood. Inspired by the millimetric bumps of the Namib Desert beetle, here we …
Understanding flow patterns and coupled transport phenomena during evaporation of droplets loaded with colloidal particles is central to design technical applications such as organizing proteins/DNA on a solid surface. We review recent reports on evaporating sessile droplets of colloidal suspensions on a solid surface. Starting from the classical mechanism of formation of a ring-like deposit, we discuss the influence of several problem parameters. Notably, thermal or solutal Marangoni effect, particle size, particle concentration, particle shape, substrate wettability, pH of the suspension etc…
A numerical method for simulating three-phase flows with moving contact lines on arbitrarily complex surfaces is developed in the framework of lattice Boltzmann method. In this method, the immiscible three-phase flow is modeled through a multiple-relaxation-time color-gradient model, which not only allows for a full range of interfacial tensions but also produces stable outcomes for a wide range of viscosity ratios. A characteristic line model is introduced to implement the wetting boundary condition, which is not only easy to implement but also able to handle arbitrarily complex boundaries wi…
